Find the inverse function of f(x)=x-2/x+2, x\=2?
回答 (2)
2015-10-07 1:46 pm
I guess you mean f(x) = (x-2)/(x+2),
and perhaps you mean x is not equal to -2.
I don't see any reason why x can't be +2.
Say y = (x-2)/(x+2), then you have
xy + 2y = x - 2, and
x(y-1) = -2(y+1), so
x = (y+1)/(1-y),
which will be valid when y is not 1.
So f^(-1) (x) = (x+1)/(x-1), valid when x is not 1.
and perhaps you mean x is not equal to -2.
I don't see any reason why x can't be +2.
Say y = (x-2)/(x+2), then you have
xy + 2y = x - 2, and
x(y-1) = -2(y+1), so
x = (y+1)/(1-y),
which will be valid when y is not 1.
So f^(-1) (x) = (x+1)/(x-1), valid when x is not 1.
2015-10-07 1:46 pm
Let y= (x-2)/(x+2)
Switch x and y
x = (y2)/(y+2)
solve for y
multiply both sides by (y+2)
x(y+2) = y-2
xy + 2x = y-2
y(x -1) = -2 -2x
y(x-1) = -2(1+x)
y = -2(x+1) / (x-1)
f^-1(x) = -2(x+1)/(x-1)
Switch x and y
x = (y2)/(y+2)
solve for y
multiply both sides by (y+2)
x(y+2) = y-2
xy + 2x = y-2
y(x -1) = -2 -2x
y(x-1) = -2(1+x)
y = -2(x+1) / (x-1)
f^-1(x) = -2(x+1)/(x-1)
收錄日期: 2021-05-04 02:48:40
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